what height of oil would lead to a gauge reading of 58.0 kpa?

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Problem 1

Perform the following estimations without using a reckoner.
(a) Guess the mass of water (kg) in an Olympic-size swimming puddle.
(b) A glass is being filled from a pitcher. Estimate the mass flow rate of the water (k/south).
(c) Twelve heavyweight boxers coincidentally get on the same elevator in Great United kingdom. Posted on the lift wall is a sign that gives the maximum condom combined weight of the passengers, $W_{\max }$ in stones (one stone $\left.=14+\mathrm{lb}_{\mathrm{1000}} \approx half dozen \mathrm{kg}\right)$ If you were 1 of the boxers, guess the everyman value of $W_{\text {max }}$ for which you lot would feel comfortable remaining on the lift.
(d) An oil pipeline across Alaska is 4.5 ft in diameter and 800 miles long. How many barrels of oil are required to fill the pipeline?
(e) Estimate the volume of your body $\left(\mathrm{cm}^{3}\right)$ in two dissimilar means. (Show your piece of work.)
(f) A solid block is dropped into h2o and very slowly sinks to the bottom. Estimate its specific gravity.

Trouble two

Summate densities in $\mathrm{Ib}_{\mathrm{1000}} / \mathrm{ft}^{3}$ of the following substances:
(a) a liquid with density of $995 \mathrm{kg} / \mathrm{chiliad}^{3}$. Use (i) conversion factors from the table on the inside front cover and (ii) Equation 3.one-2.
(b) a solid with a specific gravity of $5.7 .$

Problem 3

The specific gravity of gasoline is approximately 0.70
(a) Make up one's mind the mass (kg) of l.0 liters of gasoline.
(b) The mass period rate of gasoline exiting a refinery tank is $1150 \mathrm{kg} / \mathrm{min}$. Estimate the volumetric flow rate in liters/s.
(c) Guess the average mass menstruation rate $\left(\mathrm{lb}_{\mathrm{thou}} / \mathrm{min}\right)$ delivered past a gasoline pump.
(d) Gasoline and kerosene (specific gravity $=0.82$ ) are composite to obtain a mixture with a specific gravity of 0.78 . Calculate the volumetric ratio (book of gasoline/book of kerosene) of the 2 compounds in the mixture, assuming $V_{\text {blend }}=V_{\text {gasoline }}+V_{\text {kerosene }}$

Problem iv

Assume the cost of gasoline in France is approximately 5 French francs per liter and the exchange rate is 5.22 francs per U.Southward. dollar. How much would you pay, in dollars, for $fifty.0 \mathrm{kg}$ of gasoline in France, assuming gasoline has a specific gravity of $0.lxx .$ What would the same quantity of gasoline cost in the United States at a rate of $\$ 1.20$ per gallon?

Problem 5

Liquid benzene and liquid $n$ -hexane are composite to course a stream flowing at a rate of $700 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}$. An on-line densitometer (an musical instrument used to decide density) indicates that the stream has a density of $0.850 \mathrm{g} / \mathrm{mL}$ Using specific gravities from Table B.1, gauge the mass and volumetric feed rates of the two hydrocarbons to the mixing vessel (in American engineering science units). State at to the lowest degree 2 assumptions required to obtain the judge from the recommended data.

Problem half-dozen

At $25^{\circ} \mathrm{C},$ an aqueous solution containing $35.0 \mathrm{wt} \% \mathrm{H}_{ii} \mathrm{And so}_{4}$ has a specific gravity of $1.2563 .$ A quantity of the $35 \%$ solution is needed that contains $195.5 \mathrm{kg}$ of $\mathrm{H}_{two} \mathrm{And then}_{iv}$
(a) Calculate the required volume (50) of the solution using the given specific gravity.
(b) Judge the percent error that would have resulted if pure-component specific gravities of $\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{SG}=1.8255)$ and water had been used for the calculation instead of the given specific gravity of the mixture.

Aadit S.

Numerade Educator

Problem seven

A rectangular cake of solid carbon (graphite) iloats at the interface of two immiscible liquids. The bottom liquid is a relatively heavy lubricating oil. and the top liquid is water. Of the full block book, $54.2 \%$ is immersed in the oil and the balance is in the water. In a dissever experiment, an empty flask is weighed, $35.3 \mathrm{cm}^{3}$ of the lubricating oil is poured into the flask, and the flask is reweighed. If the scale reading was $124.8 \mathrm{g}$ in the first weighing, what would it be in the second weighing? (Proposition: Think Archimedes' principle, and do a force balance on the block.)

Problem 8

A rectangular block floats in pure h2o with 0.5 in. above the surface and 1.5 in. below the surface. When placed in an aqueous solution, the cake of material floats with one in. below the surface. Estimate the specific gravities of the block and the solution. (Suggestion: Call the horizontal cross sectional surface area of the cake $A$. $A$ should cancel in your calculations.)

Problem 9

An object of density $\rho_{\mathrm{a}},$ volume $V_{\mathrm{a}},$ and weight $W_{\mathrm{a}}$ is thrown from a rowboat floating on the surface of a modest pond and sinks to the bottom. The weight of the rowboat without the jettisoned object is $W_{\mathrm{b}} .$ Before the object was thrown out, the depth of the swimming was $h_{\mathrm{pl}},$ and the bottom of the gunkhole was a distance $h_{b 1}$ to a higher place the pond lesser. Afterward the object sinks, the values of these quantities are $h_{\mathrm{p} ii}$ and $h_{\mathrm{b} 2} .$ The expanse of the swimming is $A_{\mathrm{p}}$; that of the boat is $A_{\mathrm{b}} . A_{\mathrm{b}}$ may be assumed constant, and then that the book of water displaced by the boat is $A_{\mathrm{b}}\left(h_{\mathrm{p}}-h_{\mathrm{b}}\right)$.
(a) Derive an expression for the modify in the pond depth $\left(h_{\mathrm{p} ii}-h_{\mathrm{p} 1}\right) .$ Does the liquid level of the pond rise or neglect, or is it indeterminate?
(b) Derive an expression for the change in the height of the bottom of the gunkhole above the bottom of the pond $\left(h_{b 2}-h_{b 1}\correct) .$ Does the gunkhole rise or fall relative to the pond bottom, or is it indeterminate?

Trouble 10

Limestone (calcium carbonate) particles are stored in $50-\mathrm{50}$ bags. The void fraction of the particulate affair is 0.30 (liter of void space per liter of full volume) and the specific gravity of solid calcium carbonate is ii.93.
(a) Judge the majority density of the bag contents ( $\mathrm{kg} \mathrm{CaCO}_{3} /$ liter of total volume).
(b) Approximate the weight ( $W$ ) of the filled bags. State what you are neglecting in your estimate.
(c) The contents of three bags are fed to a ball mill, a device something like a rotating clothes dryer containing steel balls. The tumbling action of the assurance crushes the limestone particles and turns them into a powder. (Meet pp. $xx-31$ of Perry'south Chemical Engineers' Handbook. seventh ed.) The limestone coming out of the mill is put dorsum into fifty -L numberless. Would the limestone (i) just fill three numberless, (ii) autumn brusque of filling iii numberless, or (iii) fill more than 3 bags? Briefly explain your answer.

Problem 11

A useful mensurate of an private'due south physical condition is the fraction of his or her body that consists of fat. This problem describes a simple technique for estimating this fraction past weighing the individual twice, once in air and once submerged in water.
(a) $\mathrm{A}$ man has trunk mass $m_{\mathrm{b}}=122.v \mathrm{kg} .$ If he stands on a calibration calibrated to read in newtons, what would the reading be? If he then stands on a calibration while he is totally submerged in water
at $30^{\circ} \mathrm{C}$ (specific gravity $=0.996$ ) and the scale reads $44.0 \mathrm{N}$, what is the volume of his body (liters)? (Hint: Recall from Archimedes' principle that the weight of a submerged object equals the weight in air minus the buoyant force on the object, which in turn equals the weight of water displaced by the object. Neglect the buoyant force of air.) What is his torso density, $\rho_{\mathrm{b}}(\mathrm{kg} / \mathrm{L}) ?$
(b) Suppose the torso is divided into fat and nonfat components, and that $X_{\mathrm{f}}$ ( (kilograms of fat/kilograms of total trunk mass) is the fraction of the total torso mass that is fat:
$$x_{\mathrm{f}}=\frac{m_{\mathrm{f}}}{m_{\mathrm{b}}}$$
Prove that
$$x_{\mathrm{f}}=\frac{\frac{1}{\rho_{\mathrm{b}}}-\frac{1}{\rho_{\mathrm{nf}}}}{\frac{1}{\rho_{\mathrm{f}}}-\frac{1}{\rho_{\mathrm{nf}}}}$$
where $\rho_{\mathrm{b}}, \rho_{\mathrm{f}},$ and $\rho_{\mathrm{nf}}$ are the boilerplate densities of the whole trunk, the fat component, and the nonfat component, respectively. [Suggestion: Starting time by labeling the masses ( $m_{\mathrm{f}}$ and $m_{\mathrm{b}}$ ) and volumes
$\left(V_{\mathrm{f}} \text { and } V_{\mathrm{b}}\right)$ of the fat component of the body and the whole torso, and and so write expressions for the three densities in terms of these quantities. Then eliminate volumes algebraically and obtain an expression for $\left.m_{t} / m_{b} \text { in terms of the densities. }^{five}\right]$
(c) If the average specific gravity of body fat is 0.9 and that of nonfat tissue is $i.i,$ what fraction of the human being's trunk in part (a) consists of fat?
(d) The body volume calculated in office (a) includes volumes occupied by gas in the digestive tract, sinuses, and lungs. The sum of the first two volumes is roughly $100 \mathrm{mL}$ and the book of the lungs is roughly ane.2 liters. The mass of the gas is negligible. Use this information to improve your estimate of $x_{f}$

Trouble 12

Aqueous solutions of the amino acid $L$ -isoleucine (Ile) are prepared by putting 100.0 grams of pure water into each of six flasks and adding different precisely weighed quantities of Ile to each flask. The densities of the solutions at $50.0 \pm 0.05^{\circ} \mathrm{C}$ are and then measured with a precision densitometer, with the following results:
$$\brainstorm{array}{|l|l|l|l|l|l|l|}
\hline r\left(\mathrm{k} \mathrm{Ile} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\right) & 0.0000 & 0.8821 & 1.7683 & ii.6412 & 3.4093 & 4.2064 \\
\hline \rho\left(\mathrm{one thousand} \text { solution } / \mathrm{cm}^{3}\right) & 0.98803 & 0.98984 & 0.99148 & 0.99297 & 0.99439 & 0.99580 \\
\hline
\end{array}$$
(a) Plot a calibration curve showing the mass ratio. $r$, as a office of solution density, $\rho$, and fit a straight line to the information to obtain an equation of the form $r=a \rho+b$
(b) The volumetric flow rate of an aqueous Ile solution at a temperature of $50^{\circ} \mathrm{C}$ is $150 \mathrm{L} / \mathrm{h}$. The density of a sample of the stream is measured at $50^{\circ} \mathrm{C}$ and found to exist $0.9940 \mathrm{yard} / \mathrm{cm}^{3} .$ Use the calibration equation to approximate the mass menses rate of Ile in the stream $(\mathrm{kg} \mathrm{Ile} / \mathrm{h})$.
(c) It has just been discovered that the thermocouple used to measure the stream temperature was poorly calibrated and the temperature was actually $47^{\circ} \mathrm{C}$. Would the Ile mass menstruation charge per unit calculated in part (b) be too loftier or too low? State whatever assumption yous make and briefly explain your reasoning.

Problem 13

Earlier a rotameter can exist used to measure an unknown flow rate, a calibration curve of flow rate versus rotameter reading must exist prepared. A calibration technique for liquids is illustrated below. A flow rate is set by adjusting the pump speed; the rotameter reading is recorded, and the effluent from the rotameter is collected in a graduated cylinder for a timed interval. The procedure is carried out twice for each of several pump settings.
(a) Assuming the liquid is h2o at $25^{\circ} \mathrm{C}$, draw a scale curve of mass menstruation charge per unit, $\dot{m}(\mathrm{kg} / \mathrm{min})$ versus rotameter reading, $R$, and use it to estimate the mass flow rate of a water stream for which the rotameter reading is $five.3 .$
(b) The mean divergence between duplicates, $\overline{D_{i}}$, provides an estimate of the standard deviation of a unmarried measurement, which was given the symbol $s_{ten}$ on p. 18 of Chapter two :
$$s_{x} \approx \frac{\sqrt{\pi}}{2} \bar{D}_{i}=0.8862 \bar{D}_{i}$$
Moreover, conviction limits on measured values can be estimated to a adept approximation using the mean deviation between duplicates. For example, if a single measurement of $Y$ yields a
value $Y_{\text {measured }}$, and then there is a $95 \%$ probability that the true value of $Y$ falls within the $95 \%$ confidence limits $\left(Y_{\text {measured }}-i.74 \bar{D}_{i}\right)$ and $\left(Y_{\text {measured }}+1.74 \bar{D}_{i}\right) .^{6}$ For a measured menstruum rate of $610 \mathrm{yard} / \mathrm{min}$, estimate the $95 \%$conviction limits on the truthful menses charge per unit.

Problem 14

How many of the following are plant in $15.0 \mathrm{kmol}$ of benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\correct) ?(\mathrm{a}) \mathrm{kg} \mathrm{C}_{six} \mathrm{H}_{vi} ;(\mathrm{b}) \mathrm{mol} \mathrm{C}_{half-dozen} \mathrm{H}_{6}$
(c) Ib-mole $C_{6} \mathrm{H}_{6}:(\mathrm{d})$ mol (g-atom) $\mathrm{C}:(\mathrm{eastward})$ mol $\mathrm{H} ;$ (f) $\mathrm{g} \mathrm{C} ;(\mathrm{g}) \mathrm{g} \mathrm{H}:(\mathrm{h})$ molecules of $\mathrm{C}_{6} \mathrm{H}_{6}$.

Problem 15

Liquid toluene is flowing through a pipe at a rate of $175 \mathrm{m}^{3} / \mathrm{h}$.
(a) What is the mass flow rate of this stream in $\mathrm{kg} / \mathrm{min} ?$
(b) What is the molar flow rate in mol/s?
(c) In fact, the answer to part (a) is merely an approximation that is almost certain to be slightly in error. What did you accept to assume to obtain the answer?

Niamat Yard.

Numerade Educator

Trouble 16

A mixture of methanol and methyl acetate contains 15.0 wt\% methanol.
(a) Using a unmarried dimensional equation, determine the g-moles of methanol in $200.0 \mathrm{kg}$ of the mixture.
(b) The flow rate of methyl acetate in the mixture is to be 100.0 lb-mole/h. What must the mixture menstruum rate exist in $\mathrm{Ib}_{\mathrm{m}} / \mathrm{h} ?$

Problem 17

The feed to an ammonia synthesis reactor contains 25 mole $\%$ nitrogen and the remainder hydrogen. The period rate of the stream is $3000 \mathrm{kg} / \mathrm{h}$. Calculate the charge per unit of flow of nitrogen into the reactor in kg/h. (Suggestion: First calculate the average molecular weight of the mixture.)

Aadit S.

Numerade Educator

Problem 18

A suspension of calcium carbonate particles in h2o flows through a pipe. Your assignment is to determine both the flow rate and the composition of this slurry. You proceed to collect the stream in a graduated cylinder for 1.00 min; you then weigh the cylinder, evaporate the collected water, and reweigh the cylinder. The following results are obtained:
Mass of empty cylinder: $65.0 \mathrm{g}$
Mass of cylinder + collected slurry: $565 \mathrm{one thousand}$
Volume collected: $455 \mathrm{mL}$
Mass of cylinder later on evaporation: $215 \mathrm{grand}$
Summate
(a) the volumetric flow charge per unit and mass catamenia rate of the suspension.
(b) the density of the suspension.
(c) the mass fraction of $\mathrm{CaCO}_{3}$ in the suspension.

Trouble 19

A mixture is 10.0 mole $\%$ ethyl alcohol, 75.0 mole $\%$ ethyl acetate $\left(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\right)$, and 15.0 mole $\%$ acetic acid. Summate the mass fractions of each compound. What is the average molecular weight of the mixture? What would be the mass $(\mathrm{kg})$ of a sample containing $25.0 \mathrm{kmol}$ of ethyl acetate?

Trouble 20

Certain solid substances, known every bit hydrated compounds, have well-defined molecular ratios of h2o to some other species, which ofttimes is a sait. For case, calcium sulfate dihydrate (unremarkably known as gypsum, $\mathrm{CaSO}_{four} \cdot two \mathrm{H}_{2} \mathrm{O}$ ), has 2 moles of water per mole of calcium sulfate; alternatively, information technology may exist said that 1 mole of gypsum consists of ane mole of calcium sulfate and two moles of water. The water in such substances is called water of hydration. (More information about hydrated salts is given in Chapter 6.) Solid gypsum is formed in a crystallizer and leaves that unit of measurement as a slurry (a suspension of solid particles in a liquid) of solid gypsum particles suspended in an aqueous $\mathrm{CaSO}_{4}$ solution. The slurry flows from the crystallizer to a filter in which the particles are collected as a filter block. The filter cake, which is $95.0 \mathrm{wt} \%$ solid gypsum and the remainder $\mathrm{CaSO}_{four}$ solution, is fed to a dryer in which all water (including the water of hydration in the crystals) is driven off to yield anhydrous (water-costless) $\mathrm{CaSO}_{four}$ as product. A flowchart and relevant process data are given beneath.
Solids content of slurry leaving crystallizer: $0.35 \mathrm{kg} \mathrm{CaSO}_{4} \cdot ii \mathrm{H}_{ii} \mathrm{O} / \mathrm{L}$ slurry $\mathrm{CaSO}_{iv}$ content of slurry liquid: $0.209 \mathrm{thou} \mathrm{CaSO}_{4} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}$
Specific gravities: $\operatorname{CaSO}_{four} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{due south}), ii.32 ;$ liquid solutions, ane.05
(a) Briefly explain in your own words the functions of the iii units (crystallizer, filter, and dryer).
(b) Accept a basis of one liter of solution leaving the crystallizer and summate the mass ( $\mathrm{kg}$ ) and volume (Fifty) of solid gypsum, the mass of $\mathrm{CaSO}_{four}$ in the gypsum, and the mass of $\mathrm{CaSO}_{four}$ in the liquid solution.
(c) Calculate the per centum recovery of $\mathrm{CaSO}_{4}-$ that is, the percent of the total $\mathrm{CaSO}_{4}$ (precipitated plus dissolved) leaving the crystallizer recovered equally solid anhydrous $\mathrm{CaSO}_{iv}$.

Trouble 21

Things were going smoothly at the Breaux Bridge Drug Co. pilot institute during the midnight to 8 a.k. shift until Therèse Lagniappe, the reactor operator, allow the run didactics sheet get too close to the Coleman stove that was being used to heat h2o to prepare Lagniappe's bihourly cup of Community Coffee. What followed ended in a total loss of the run sheet. the java. and a substantial portion of the novel Lagniappe was writing. Remembering the less than enthusiastic reaction she got the last fourth dimension she telephoned her supervisor in the middle of the night. Lagniappe decided to rely on her memory of the required flow-rate settings. The two liquids being fed to a stirred-tank reactor were circulostoic acid (CSA: $M W=$ 75, SG = 0.ninety) and flubitol (FB: MW = 90, SG = 0.75). The product from the system was a popular over-the-counter drug that simultaneously cures loftier blood pressure and clumsiness. The molar ratio of the two feed streams had to be betwixt 1.05 and i.10 mol $\mathrm{CSA} / \mathrm{mol}$ FB to keep the contents of the reactor from forming a solid plug. At the time of the accident, the flow rate of CSA was
$45.8 \mathrm{L} / \mathrm{min} .$ Lagniappe set the catamenia of flubitol to the value she thought had been in the run sheet: 55.2 Fifty/min. Was she right? If not, how would she accept been likely to learn of her mistake? (Annotation: The reactor was stainless steel, so she could not encounter the contents.)

Trouble 22

A mixture of ethanol (ethyl alcohol) and h2o contains $60.0 \%$ water past mass.
(a) Assuming volume additivity of the components, estimate the specific gravity of the mixture at $20^{\circ} \mathrm{C} .$ What volume (in liters) of this mixture is required to provide 150 mol of ethanol?
(b) Echo role (a) with the additional information that the specific gravity of the mixture at $xx^{\circ} \mathrm{C}$ is 0.93518 (making it unnecessary to assume book additivity). What percentage error results from the book additivity assumption?

Problem 23

A mixture of marsh gas and air is capable of beingness ignited only if the mole percent of methyl hydride is betwixt $5 \%$ and $fifteen \% .$ A mixture containing nine.0 mole $\%$ methane in air flowing at a rate of $700 . \mathrm{kg} / \mathrm{h}$ is to be diluted with pure air to reduce the methane concentration to the lower flammability limit. Calculate the required catamenia charge per unit of air in mol/h and the per centum by mass of oxygen in the production gas. (Note: Air may be taken to consist of 21 mole $\% \mathrm{O}_{2}$ and $79 \% \mathrm{N}_{two}$ and to accept an average molecular weight of 29.0.)

Problem 24

A liquid mixture is prepared past combining $Northward$ different liquids with densities $\rho_{1}, \rho_{2}, \ldots, \rho_{N}$ The volume of component $i$ added to the mixture is $V_{i}$ and the mass fraction of this component in the mixture is $x_{i} .$ The components are completely miscible.
Determine which of the following two formulas should exist used to estimate the density of the liquid mixture, $\bar{\rho}$, if the volume of the mixture equals the sum of the pure-component volumes.
$$\vec{\rho}=\sum_{i=1}^{N} x_{i} \rho_{i} \quad \text { (A) } \quad \frac{1}{\bar{\rho}}=\sum_{i=ane}^{N} \frac{x_{i}}{\rho_{i}}\quad (B)$$
Decide whether $(\mathrm{A})$ or $(\mathrm{B})$ is the correct formula (testify your proof), and and then utilise the correct formula to estimate the density ( $\mathrm{g} / \mathrm{cm}^{3}$ ) of a liquid mixture containing $lx.0 \mathrm{wt} \%$ acetone, $25.0 \mathrm{wt} \%$ acetic acrid, and $15.0 \mathrm{wt} \%$ carbon tetrachloride.

Problem 25

A gaseous mixture of $\mathrm{CO}, \mathrm{CO}_{ii}, \mathrm{CH}_{4},$ and $\mathrm{N}_{2}$ is analyzed with a gas chromatograph (see Problem 3.26). The output appears on a strip-chart recorder, as shown hither.
For each of the three species, the area under the peak is approximately proportional to the number of moles of the indicated substance in the sample. From other data, it is known that the molar ratio of methane $\left(\mathrm{CH}_{four}\right)$ to nitrogen is 0.200 .
(a) What are the mole fractions of the four species in the gas?
(b) What is the average molecular weight of the gas?

Problem 26

A gas chromatograph (GC) is a device used to split up the components of a sample of a gas or liquid mixture and to provide a measure of the amount of each component in the sample. The output from a chromatographic analysis typically takes the course of a series of peaks on a strip-chart recorder. (See the preceding problem.) Each peak corresponds to a specific component, and the expanse under the elevation is proportional to the amount of that component in the sample $\left[n_{i}(\mathrm{mol})=k_{i} A_{i}\right.$ where $A_{i}$ is the surface area of the peak corresponding to the $i \text { th species }]$ The proportionality constants $\left(k_{i}\right)$ are determined in separate calibration experiments in which known amounts of the components are injected into the GC sample port and the corresponding peak areas are measured.
(a) Gear up a spreadsheet to summate the composition of a mixture from a set of tiptop areas obtained from a chromatograph. The spreadsheet should appear as follows:
You may utilise additional columns to shop intermediate quantities in the calculation of the mass and mole fractions. In the bodily spreadsheet, the dashes ( $-$ ) would exist replaced by numbers. Examination your program on data for five mixtures of methane, ethane, propane, and $n$ -butane. The $m$ values for these species are those given in the above table, and the measured peaks are given beneath. For example, the area of the methane height for the first mixture is $3.6,$ the area of the ethane meridian for the same mixture is $2.8,$ and so on.
(b) Write a figurer plan (non a spreadsheet) to perform the aforementioned task- -that is, calculate mole and mass fractions from measured chromatographic pinnacle areas. The plan should perform the following steps:
i. read in $North,$ the number of species to exist analyzed;
i. read in $M_{1}, M_{two}, M_{3}, \ldots, M_{N},$ the molecular weights of the species;
3. read in $k_{1}, k_{2}, k_{iii}, \ldots, k_{N},$ the scale constants for the species;
four. read in $N_{d}$, the number of chromatographic analyses performed;
v. for the start assay, read in the measured pinnacle areas $A_{1}, A_{ii}, A_{3}, \ldots, A_{N}$
vi. calculate and print out the sample number, the mole fractions of each species in the sample. and the mass fractions of each species in the sample;
vii Repeat steps v and 6 for each of the remaining analyses. Exam your program on the 5 sample data set given in role (a).

Trouble 27

Biomass combustion-burning of forests, grasslands, agricultural wastes, and other biological thing--is recognized as a serious threat to the environment? The table below shows the distribution of carbon-containing compounds released to the atmosphere worldwide from all combustion sources as well every bit the portion coming from biomass burning.
$$\begin{assortment}{ccc}
\hline & \text { Metric Tons C, } & \text { Metric Tons C, } \\
\text { Compound } & \text { All Sources } & \text { % from Biomass } \\
\hline \mathrm{CO}_{2} & 8700 & 40 \\
\mathrm{CO} & 1100 & 26 \\
\mathrm{CH}_{4} & 380 & x \\
\hline
\cease{array}$$
The numbers in the center column reflect almanac quantities of carbon released to the atmosphere
in the indicated chemical compound; for example. 8700 metric tons of carbon $\left(8.7 \times 10^{half dozen} \mathrm{kg} \mathrm{C}\right)$ was released
in carbon dioxide.
(a) Determine the combined almanac release (in metric tons) of all three species resulting from biomass combustion and the boilerplate molecular weight of the combined gases.
(b) Find a reference on atmospheric pollution and list the ecology hazards associated with CO and $\mathrm{CO}_{2}$ release. What other elements might be released in environmentally hazardous forms if biomass is burned?

Trouble 28

A 5.00 -wt $\%$ aqueous sulfuric acid solution $(\rho=1.03 \mathrm{g} / \mathrm{mL})$ flows through a $45-\mathrm{m}$ long pipage with a 6.0 cm bore at a rate of $87 \mathrm{L} / \mathrm{min}$.
(a) What is the molarity of sulfuric acid in the solution?
(b) How long (in seconds) would it take to fill a 55-gallon drum, and how much sulfuric acid ( $\left(\mathrm{b}_{\mathrm{m}}\right)$ would the drum contain? (You lot should get in at your answers with two dimensional equations.)
(c) The hateful velocity of a fluid in a pipe equals the volumetric menstruum charge per unit divided by the crosssectional expanse normal to the direction of menstruation. Utilise this information to judge how long (in seconds) it takes the solution to flow from the pipe inlet to the outlet.

Problem 29

A gas stream contains 18.0 mole $\%$ hexane and the balance nitrogen. The stream flows to a condenser, where its temperature is reduced and some of the hexane is liquefied. The hexane mole fraction in the gas stream leaving the condenser is 0.0500 . Liquid hexane condensate is recovered at a rate of $1.50 \mathrm{L} / \mathrm{min}$.
(a) What is the flow rate of the gas stream leaving the condenser in mol/min? (Hint: First summate the molar flow rate of the condensate and note that the rates at which $C_{6} \mathrm{H}_{14}$ and $\mathrm{N}_{ii}$ enter the unit must equal the total rates at which they get out in the two get out streams.)
(b) What percentage of the hexane entering the condenser is recovered as a liquid?

Rashmi S.

Numerade Educator

Problem xxx

The little-known rare earth chemical element nauseum (diminutive weight $=172$ ) has the interesting property of being completely insoluble in everything but 12 -twelvemonth-old bourbon. This curious fact was discovered in the laboratory of Professor Ludwig von Schlimazel, the eminent German chemist whose invention of the bathtub band won him the Nobel Prize. Having unsuccessfully tried to dissolve nauseum in 7642 different solvents over a 10 -year period, Schlimazel finally came to the 30 mL of Former Aardvark Bottled-in-Bond that was the only remaining liquid in his laboratory. Always willing to endure personal loss in the proper noun of science, Schlimazel calculated the amount of nauseum needed to make upwardly a 0.03 molar solution, put the Aardvark bottle on the desk of his true-blue technician Edgar
P. Settera, weighed out the calculated amount of nauseum and put it side by side to the canteen, and then wrote the message that has become office of history:
"Ed Settera. Add nauseum!"
How many grams of nauseum did he weigh out? (Neglect the change in liquid volume resulting from the nauseum addition.)

Trouble 31

The reaction $\mathrm{A} \rightarrow \mathrm{B}$ is carried out in a laboratory reactor. According to a published commodity the concentration of A should vary with fourth dimension as follows:
$$C_{\mathrm{A}}=C_{\mathrm{AO}} \exp (-k t)$$
where $C_{\mathrm{AO}}$ is the initial concentration of $\mathrm{A}$ in the reactor and $k$ is a constant.
(a) If $C_{\mathrm{A}}$ and $C_{\mathrm{AO}}$ are in $\mathrm{lb}$ -moles/ft $^{iii}$ and $t$ is in minutes, what are the units of $chiliad ?$
(b) The following data are taken for $C_{\mathrm{A}}(t)$
$$\begin{assortment}{cc}
\hline t(\min ) & C_{\mathrm{A}}\left(\mathrm{lb}-\mathrm{mole} / \mathrm{ft}^{3}\right) \\
\hline 0.five & 1.02 \\
one.0 & 0.84 \\
1.v & 0.69 \\
two.0 & 0.56 \\
iii.0 & 0.38 \\
5.0 & 0.17 \\
10.0 & 0.02 \\
\hline
\cease{array}$$
Verify the proposed rate law graphically (starting time make up one's mind what plot should yield a straight line), and summate $C_{\mathrm{AO}}$ and $grand$
(c) Convert the formula with the calculated constants included to an expression for the molarity of A in the reaction mixture in terms of $t$ (seconds). Calculate the molarity at $t=200$ s.

Trouble 32

Perform the post-obit pressure conversions, assuming when necessary that atmospheric pressure is one atm. Unless otherwise stated, the given pressures are accented.
(a) $2600 \mathrm{mm}$ Hg to psi
(b) $275 \mathrm{ft} \mathrm{H}_{2} \mathrm{O}$ to $\mathrm{kPa}$
(c) 3.00 atm to North/cm $^{ii}$
(d) $280 \mathrm{cm} \mathrm{Hg}$ to dyne/k $^{2}$
(due east) $20 \mathrm{cm}$ Hg of vacuum to atm (absolute)
(f) 25.0 psig to mm Hg (gauge)
(g) 25.0 psig to mm Hg (absolute)
(h) $325 \mathrm{mm}$ Hg to mm Hg guess
(i) 35.0 psi to cm of carbon tetrachloride

Problem 33

A storage tank containing oil ( $\mathrm{SG}=0.92$ ) is 10.0 meters high and 16.0 meters in diameter. The tank is closed, merely the amount of oil it contains can be adamant from the judge pressure at the bottom.
(a) A pressure estimate connected to the bottom of the tank was calibrated with the superlative of the tank open to the atmosphere. The calibration curve is a plot of height of oil, $h(\mathrm{m}),$ versus $P_{\text {estimate }}(\mathrm{kPa})$ Sketch the expected shape of this plot. What elevation of oil would pb to a gauge reading of 68 kPa? What would be the mass ( $\mathrm{kg}$ ) of oil in the tank corresponding to this height?
(b) An operator observes that the force per unit area approximate reading is $68 \mathrm{kPa}$ and notes the corresponding liquid height from the scale curve. What he did non know was that the absolute pressure in a higher place the liquid surface in the tank was $115 \mathrm{kPa}$ when he read the approximate. What is the bodily height of the oil? (Assume atmospheric pressure is $101 \mathrm{kPa}$.)

Problem 34

A rectanguiar biock of height $L$ and horizontal cross-sectional area $A$ floats at the interface between two immiscible liquids, as shown below.
(a) Derive a formula for the block density, $\rho_{half dozen},$ in terms of the fluid densities $\rho_{1}$ and $\rho_{ii},$ the heights $h_{0}$ $h_{1},$ and $h_{2},$ and the cross-sectional expanse $A$. (It is not necessary that all of these variables announced in the terminal effect.)
(b) Forcefulness balances on the block can be calculated in ii ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) in terms of the weight of the cake and the buoyant force on the block every bit expressed past Archimedes' principle. Prove that these ii approaches are equivalent.

Problem 35

The viewing window in a diving suit has an area of roughly $65 \mathrm{cm}^{2}$. If an try were made to maintain the pressure on the inside of the suit at 1 atm, what force $\left(\mathrm{N} \text { and } \mathrm{lb}_{\mathrm{f}}\right)$ would the window have to withstand if the diver descended to a depth of 150 m. Have the specific gravity of the water to be 1.05.

Trouble 36

The slap-up Boston molasses overflowing occurred on January $fifteen,1919 .$ In it, 2.3 one thousand thousand gallons of crude molasses flowed from a 30-foot high storage tank that ruptured, killing 21 people and injuring 150. The estimated specific gravity of crude molasses is $ane.4 .$ What were the mass of molasses in the tank in $\mathrm{lb}_{\mathrm{m}}$ and the pressure at the bottom of the tank in $\mathrm{lb}_{\mathrm{f}} / \mathrm{in} .^{2} ?$ Give at to the lowest degree two possible causes of the tragedy.

Problem 37

The chemical reactor shown below has a comprehend (called a head) that is held in place by a serial of bolts. The caput is fabricated of stainless steel $(\mathrm{SG}=8.0)$, is iii in. thick, has a diameter of 24 in... and covers and seals an opening twenty in. in bore. During turnaround, when the reactor is taken out of service for cleaning and repair, the head was removed past an operator who thought the reactor had been depressurized using a standard venting procedure. However, the pressure guess had been damaged in an earlier process upset (the reactor pressure had exceeded the upper limit of the gauge), and instead of being depressurized completely, the vessel was under a gauge pressure of 30 psi.
(a) What force ( $\left(\mathrm{lb}_{\mathrm{f}}\right)$ were the bolts exerting on the caput before they were removed? (Hint: Don't forget that a pressure is exerted on the tiptop of the caput by the atmosphere.) What happened when the last bolt was removed by the operator? Justify your prediction past estimating the initial dispatch of the head upon removal of the last bolt.
(b) Advise an alteration in the turnaround process to foreclose recurrence of an incident of this kind.

Trouble 38

In the flick The Drowning Puddle, individual detective Lew Harper (played by Paul Newman) is trapped
by the bad guy in a room containing a swimming pool. The room may exist considered rectangular, five meters wide by fifteen meters long, with an open up skylight window x meters above the floor. In that location is a single entry to the room. reached by a stairway: a locked ii-m high by 1-yard wide door, whose bottom is 1 meter above the floor. Harper knows that his enemy will return in eight hours and decides he can escape past filling the room with water and floating up to the skylight. He plugs the drain with his clothes, turns on the h2o valves, and prepares to put his plan into activity.
(a) Prove that if the door is completely under h2o and $h$ is the altitude from the top of the door to the surface of the water, so the internet force exerted on the door satisfies the inequality $$F>\rho_{\mathrm{H}_{2} \mathrm{O}} one thousand h A_{\mathrm{door}}$$ (Don't forget that a pressure is besides exerted on the door by the outside air.)
(b) Assume that water enters the room at about 5 times the charge per unit at which information technology enters an average bathtub and that the door tin withstand a maximum forcefulness of 4500 newtons (near $1000 \mathrm{lb}_{\mathrm{f}}$ ). Estimate (i) whether the door will break before the room fills and (2) whether Harper has time to escape if the door holds. Land whatever assumptions you make.

Problem 39

A housing development is served by a water tower with the water level maintained between 20 and 30 meters in a higher place the ground, depending on demand and water availability. Responding to a resident'south complaint most the low menstruum rate of h2o at his kitchen sink, a representative of the developer came and measured the water pressure at the tap higher up the kitchen sink and at the junction between the water main (a pipe connected to the bottom of the water tower) and the feed pipe to the house. The junction is $5 \mathrm{one thousand}$ below the level of the kitchen tap. All water valves in the business firm were turned off.
(a) If the water level in the tower was $25 \mathrm{g}$ above tap level, what should be the gauge pressures (kPa) at the tap and junction?
(b) Suppose the pressure measurement at the tap was lower than your estimate in role (a), but the measurement at the junction was as predicted. Land a possible explanation.
(c) If pressure measurements corresponded to the predictions in part (a), what else could be responsible for the depression water flow to the sink?

Problem 40

Two mercury manometers, one open-end and the other sealed-end, are attached to an air duct. The reading on the open-end manometer is $25 \mathrm{mm}$ and that on the sealed-cease manometer is $800 \mathrm{mm}$. Determine the absolute force per unit area in the duct, the estimate pressure in the duct, and the atmospheric force per unit area, all in mm Hg.

Trouble 41

Three different liquids are used in the manometer shown hither.
(a) Derive an expression for $P_{i}-P_{2}$ in terms of $\rho_{\mathrm{A}}, \rho_{\mathrm{B}}, \rho_{\mathrm{C}}, h_{1},$ and $h_{ii}$
(b) Suppose fluid A is methanol, $\mathrm{B}$ is h2o, and $\mathrm{C}$ is a manometer fluid with a specific gravity $1.37 ;$ pressure $P_{2}=121.0 \mathrm{kPa} ; h_{one}=xxx.0 \mathrm{cm} ;$ and $h_{ii}=24.0 \mathrm{cm} .$ Calculate $P_{1}(\mathrm{kPa})$

Aadit S.

Numerade Educator

Problem 42

The level of toluene (a flammable hydrocarbon) in a storage tank may fluctuate between 10 and $400 \mathrm{cm}$ from the superlative of the tank. since it is impossible to come across inside the tank, an open up-end manometer with water or mercury as the manometer fluid is to be used to make up one's mind the toluene level. One leg of the manometer is attached to the tank $500 \mathrm{cm}$ from the pinnacle. A nitrogen blanket at atmospheric pressure is maintained over the tank contents.
(a) When the toluene level in the tank is $150 \mathrm{cm}$ below the top $(h=150 \mathrm{cm})$, the manometer fluid level in the open arm is at the tiptop of the signal where the manometer connects to the tank. What manometer reading, $R$ (cm), would be observed if the manometer fluid is (i) mercury, (2) h2o? Which manometer fluid would you utilise, and why?
(b) Briefly draw how the system would work if the manometer were simply filled with toluene. Requite several advantages of using the fluid y'all chose in part (a) over using toluene.
(c) What is the purpose of the nitrogen blanket?

Aadit Due south.

Numerade Educator

Problem 43

A fluid of unknown density is used in two manometers - one sealed-end, the other beyond an orifice in a water pipeline. The readings shown hither are obtained on a day when barometric pressure level is $756 \mathrm{mm} \mathrm{Hg}$
What is the pressure drop (mm Hg) from betoken ( $a$ ) to point $(b) ?$

Aadit South.

Numerade Educator

Trouble 44

An open-end mercury manometer is connected to a low-pressure level pipeline that supplies a gas to a laboratory. Because pigment was spilled on the arm connected to the line during a laboratory renovation, it is impossible to run across the level of the manometer fluid in this arm. During a period when the gas supply is continued to the line but there is no gas catamenia, a Bourdon gauge connected to the line downstream from the manometer gives a reading of 7.five psig. The level of mercury in the open arm is $900 \mathrm{mm}$ to a higher place the lowest part of the manometer.
(a) When the gas is non flowing, the pressure is the same everywhere in the pipe. How high above the bottom of the manometer would the mercury be in the arm connected to the pipe?
(b) When gas is flowing, the mercury level in the visible arm drops by $25 \mathrm{mm}$. What is the gas pressure (psig) at this moment?

Aadit Due south.

Numerade Educator

Problem 45

An inclined manometer is a useful device for measuring small pressure differences. The formula given in Department 3.4 for the pressure difference in terms of the liquid-level divergence h remains valid, but while $h$ would be small and hard to read for a small pressure drop if the manometer were vertical, $L$ tin can exist made quite large for the same pressure level drop by making the angle of the inclination, $\theta$, small.
(a) Derive a formula for $h$ in terms of $L$ and $\theta$.
(b) Suppose the manometer fluid is water, the process fluid is a gas, the inclination of the manometer is $\theta=fifteen^{\circ},$ and a reading $L=8.7 \mathrm{cm}$ is obtained. What is the force per unit area difference between points ? and ??

Trouble 46

An open up-end mercury manometer is to be used to measure the pressure in an appliance containing a vapor that reacts with mercury. A x cm layer of silicon oil $(Southward G=0.92)$ is placed on top of the mercury in the arm fastened to the apparatus. Atmospheric pressure is $765 \mathrm{mm} \mathrm{Hg}$.
(a) If the level of mercury in the open end is 365 mm below the mercury level in the other arm, what is the pressure (mm Hg) in the apparatus?
(b) When the instrumentation specialist was deciding on a liquid to put in the manometer, she listed several properties the fluid should have and eventually selected silicon oil. What might the listed properties have been?

Problem 47

An orifice meter (encounter Figure $3.2-1$ ) is to be calibrated for the measurement of the flow charge per unit of stream of liquid acetone. The differential manometer fluid has a specific gravity of $1.10 .$
The scale is accomplished by connecting the orifice meter in series with a rotameter that has previously been calibrated for acetone, adjusting a valve to set the flow rate, and recording the flow rate (determined from the rotameter reading and the rotameter calibration curve) and the differential manometer reading, $h$. The procedure is repeated for several valve settings to generate an orifice meter calibration curve of flow rate versus $h$. The post-obit data are taken.
$$\begin{assortment}{cc}
\hline \brainstorm{array}{c}
\text { Manometer Reading } \\
\mathrm{h}(\mathrm{mm})
\stop{array} & \begin{array}{c}
\text { Catamenia Rate } \\
\dot{V}(\mathrm{mL} / \mathrm{s})
\stop{array} \\
\hline 0 & 0 \\
5 & 62 \\
ten & 87 \\
xv & 107 \\
20 & 123 \\
25 & 138 \\
30 & 151 \\
\hline
\end{array}$$
(a) For each of the given readings, summate the pressure driblet across the orifice, $\Delta P(\mathrm{mm} \mathrm{Hg})$.
(b) The flow charge per unit through an orifice should be related to the pressure drop across the orifice past the formula $$\dot{V}=K(\Delta P)^{northward}$$ Verify graphically that the given orifice scale data are correlated by this human relationship, and determine the values of $K$ and $n$ that best fit the data.
(c) Suppose the orifice meter is mounted in a procedure line containing acetone and a reading $h=23$ mm is obtained. Determine the volumetric, mass, and molar menstruum rates of acetone in the line.

Problem 48

Convert the temperatures in parts (a) and (b) and temperature intervals in parts (c) and (d):
(a) $T=85^{\circ} \mathrm{F}$ to $^{\circ} \mathrm{R},^{\circ} \mathrm{C}, \mathrm{Chiliad}$
(b) $T=-ten^{\circ} \mathrm{C}$ to $\mathrm{1000},^{\circ} \mathrm{F},^{\circ} \mathrm{R}$
(c) $\Delta T=85^{\circ} \mathrm{C}$ to $\mathrm{K},^{\circ} \mathrm{F},^{\circ} \mathrm{R}$
(d) $\Delta T=150^{\circ} \mathrm{R}$ to $^{\circ} \mathrm{F},^{\circ} \mathrm{C}, \mathrm{K}$

Aadit S.

Numerade Educator

Problem 49

A temperature calibration that never quite defenseless on was formulated past the Austrian chemist Johann Sebastian Farblunget. The reference points on this calibration were $0^{\circ} \mathrm{FB}$, the temperature below which Farblunget's postnasai baste began to bother him, and $1000^{\circ} \mathrm{FB}$, the boiling point of beer. Conversions between $^{\circ} \mathrm{C}$ and $^{\circ} \mathrm{FB}$ can be achieved with the expression
$$T\left(^{\circ} \mathrm{C}\right)=0.0940 T\left(^{\circ} \mathrm{FB}\right)+4.00$$
Louis Louis. Farblunget'due south French nephew, attempted to follow in his uncle's footsteps by formulating his own temperature scale. He divers the degree Louie using as reference weather condition the optimum serving temperature of marinated snails $\left(100^{\circ} \mathrm{L} \text { corresponding to } xv^{\circ} \mathrm{C}\right)$and the temperature at which the rubberband in his briefs began to relax ( $k^{\circ} \mathrm{L}$ corresponding to $43^{\circ} \mathrm{C}$ ).
(a) At what temperature in "F does beer boil?
(b) What is the temperature interval of ten.0 Farblunget degrees equivalent to in $^{\circ} \mathrm{C}, \mathrm{Thou},^{\circ} \mathrm{F},$ and $^{\circ} \mathrm{R} ?$
(c) Derive equations for $T\left(^{\circ} \mathrm{C}\right)$ in terms of $T\left(^{\circ} \mathrm{L}\right)$ (run into Example $3.5-1$ ) and $T\left(^{\circ} \mathrm{L}\right)$ in terms of $T\left(^{\circ} \mathrm{FB}\right)$
(d) What is the boiling point of ethane at ane atm (Table B.1) in $^{\circ} \mathrm{F}, \mathrm{Yard},^{\circ} \mathrm{R},^{\circ} \mathrm{FB},$ and $^{\circ} \mathrm{L} ?$
(e) What is a temperature interval of l.0 Louie degrees equivalent to in Celsius degrees, Kelvin degrees, Fahrenheit degrees, Rankine degrees, and Farblunget degrees?

Problem 50

A thermocouple is a temperature-measurement device that consists of two different metal wires joined at 1 terminate. An oversimplified diagram follows.
A voltage generated at the metal junction is read on a potentiometer or millivoltmeter. When certain metals are used, the voltage varies linearly with the temperature at the junction of the two metals:
$$5(\mathrm{mV})=a T\left(^{\circ} \mathrm{C}\right)+b$$
An iron-constantan thermocouple (constantan is an alloy of copper and nickel) is calibrated past inserting its junction in boiling water and measuring a voltage $V=5.27 \mathrm{mV},$ and so inserting the junction in silver chloride at its melting point and measuring $5=24.88 \mathrm{mV}$
(a) Derive the linear equation for $V(\mathrm{mV})$ in terms of $T\left(^{\circ} \mathrm{C}\right)$. And so convert it to an equation for $T$ in terms of $V$.
(b) If the thermocouple is mounted in a chemical reactor and the voltage is observed to go from x.0 $\mathrm{mV}$ to $thirteen.6 \mathrm{mV}$ in $20 \mathrm{south}$, what is the boilerplate value of the rate of change of temperature. $d T / d t$ during the measurement period?

Problem 51

A thermostat control with dial markings from 0 to 100 is used to regulate the temperature of an oil bathroom. A calibration plot on logarithmic coordinates of the temperature, $T\left(^{\circ} \mathrm{F}\right)$, versus the dial setting, $R,$ is a directly line that passes through the points $\left(R_{1}=20.0, T_{1}=110.0^{\circ} \mathrm{F}\right)$ and $\left(R_{two}=\right.$ $\left.40.0, T_{two}=250.0^{\circ} \mathrm{F}\right)$
(a) Derive an equation for $T\left(^{\circ} \mathrm{F}\right)$ in terms of $R$
(b) Estimate the thermostat setting needed to obtain a temperature of $320^{\circ} \mathrm{F}$.
(c) Suppose you lot set the thermostat to the value of $R$ calculated in part (b) and the reading of a thermocouple mounted in the bath equilibrates at $295^{\circ} \mathrm{F}$ instead of $320^{\circ} \mathrm{F}$. Suggest several possible explanations.

Problem 52

Every bit will exist discussed in detail in Chapter $5,$ the ideal gas equation of land relates absolute pressure, $P(\text { atm }) ;$ gas book, $V(\text { liters }) ;$ number of moles of gas, $n(\text { mol }) ;$ and accented temperature, $T(\mathrm{K}):$
$$P V=0.08206 n T$$
(a) Convert the equation to i relating $P(\mathrm{psig}), V\left(\mathrm{ft}^{three}\right), due north(\mathrm{lb}-\mathrm{mole}),$ and $T\left(^{\circ} \mathrm{F}\right)$
(b) A thirty.0 mole $\%$ CO and seventy.0 mole $\% \mathrm{N}_{two}$ gas mixture is stored in a cylinder with a volume of 3.5 $\mathrm{ft}^{three}$ at a temperature of $85^{5} \mathrm{F.}$ The reading on a Bourdon estimate fastened to the cylinder is $500 \mathrm{psi}$. Calculate the total amount of gas (lb-mole) and the mass of $\mathrm{CO}\left(\mathrm{lb}_{\mathrm{one thousand}}\right)$ in the tank.
(c) Approximately to what temperature ( $^{\circ} \mathrm{F}$ ) would the cylinder take to exist heated to increase the gas pressure to 3000 psig, the rated prophylactic limit of the cylinder? (The gauge would but be guess because the ideal gas equation of country would not be accurate at pressures this loftier.)

Problem 53

Streams of methane and air (79 mole \% $\mathrm{Due north}_{2}$, the residual $\mathrm{O}_{two}$ ) are combined at the inlet of a combustion furnace preheater. The pressures of each stream are measured with open-end mercury manometers, the temperatures are measured with resistance thermometers, and the volumetric menstruum rates are measured with orifice meters.
Data:
Flowmeter $1: \quad V_{1}=947 \mathrm{m}^{3} / \mathrm{h}$
Flowmeter $two: \quad V_{2}=195 \mathrm{m}^{3} / \mathrm{min}$
Manometer $ane: \quad h_{i}=232 \mathrm{mm}$
Manometer $2: \quad h_{2}=156 \mathrm{mm}$
Manometer 3: $\quad h_{iii}=74 \mathrm{mm}$ Resistance thermometer $1: \quad r_{1}=26.159$ ohms Resistance thermometer $2: \quad r_{two}=26.157$ ohms Resistance thermometer $three: \quad r_{3}=44.789$ ohms Atmospheric pressure: A sealed-cease mercury manometer reads $h=29.76$ in.
The resistance thermometers were calibrated by measuring their resistances at the freezing and boiling points of water, with the following results:
$$\brainstorm{array}{ll}
T=0^{\circ} \mathrm{C}: & r=23.624 \mathrm{ohms} \\
T=100^{\circ} \mathrm{C}: & r=33.028 \mathrm{ohms}
\end{array}$$
A directly-line relationship between $T$ and $r$ may be assumed. The relationship betwixt the full molar flow rate of a gas and its volumetric flow charge per unit is, to a practiced approximation, given by a form of the ideal gas equation of state:
$$\dot{n}\left(\frac{\mathrm{kmol}}{southward}\right)=\frac{12.186 P(\mathrm{atm}) \dot{Five}\left(\mathrm{m}^{3} / \mathrm{s}\right)}{T(\mathrm{M})}$$
where $P$ is the absolute pressure of the gas.
(a) Derive the resistance thermometer calibration formula for $T\left(^{\circ} \mathrm{C}\correct)$ in terms of $r(\text { ohm })$
(b) Convert the given gas law expressions to an expression for $\dot{n}(\mathrm{kmol} / \mathrm{min})$ in terms of $P(\mathrm{mm} \mathrm{Hg}), T\left(^{\circ} \mathrm{C}\right),$ and $\dot{5}\left(\mathrm{thousand}^{3} / \mathrm{min}\right)$
(c) Calculate the temperatures and pressures at points $ane,2,$ and 3
(d) Calculate the molar flow charge per unit of the combined gas stream.
(e) Calculate the reading of flowmeter 3 in $grand^{iii} /$ min.
(f) Calculate the total mass flow rate and the mass fraction of the marsh gas at indicate three .

Problem 54

You lot are performing an experiment in which the concentration, $C_{\mathrm{A}},$ of a reactive species is measured equally a function of time, $t,$ at several temperatures, $T$. At a fixed temperature, $C_{\mathrm{A}}$ varies with $t$ according to the relation $$1 / C_{\mathrm{A}}=1 / C_{\mathrm{A} 0}+k t$$
where $C_{\mathrm{A}}(\text { mol/liter })$ is the concentration of $\mathrm{A}$ at time $t(\mathrm{min}), C_{\mathrm{A} 0}(\mathrm{mol} / \text { liter })$ is the inital concentration of $\mathrm{A},$ and $g[\mathrm{50} /(\mathrm{mol} \cdot \mathrm{min})]$ is the reaction charge per unit constant. The rate abiding in turn depends on temperature, according to the formula $$k=k_{0} \exp [-E /(viii.314 T)]$$ where $k_{0}$ is a contant, $T(\mathrm{Grand})$ is the reactor temperature, and $East(\mathrm{J} / \mathrm{mol})$ is the reaction activation energy.
Write a estimator program that volition carry out the following tasks:
(a) Read in $M_{\mathrm{A}}$, the molecular weight of $\mathrm{A},$ and $N_{\mathrm{T}}$, the number of temperatures at which measurements were made.
(b) For the first temperature, read in the value of $T$ in $^{\circ} \mathrm{C}$, the number of data points, $N$; and the concentrations and times $\left(t_{i}, C_{\mathrm{A} 1}\correct),\left(t_{2}, C_{\mathrm{A} two}\right), \ldots,\left(t_{n}, C_{A northward}\right),$ where the times are in minutes and the concentrations are in grams of A/liter.
(c) Convert the temperature to kelvin and the concentrations to mol A/L.
(d) Utilise the method of least squares (Appendix A.1) in conjunction with Equation 1 to detect the value of $one thousand$ that best fits the data. (Hint: First cast the equation in the form $y=chiliad x+b$.) Store the values of $one thousand$ and $T$ in arrays.
(due east) Impress out in a neat format the values of $T(\mathrm{One thousand}),$ the converted concentrations (mol/50) and times, and $k$
(f) Repeat steps (b) through (d) for the other temperatures.
[For extra credit: Employ the method of to the lowest degree squares once again in conjunction with Equation 2 to determine the value of $Due east$ that best fits the calculated $(T, k)$ values. Again, starting time past casting Equation two in the form $y=a 10+b .]$ It will be user-friendly to perform the to the lowest degree-squares slope calculation in a subroutine, since information technology must be washed repeatedly. Test your program on the following data:
$$M_{\mathrm{A}}=65.0 \mathrm{k} / \mathrm{mol}$$
$$\begin{array}{ccccc}
\hline & T=94^{\circ} \mathrm{C} & T=110^{\circ} \mathrm{C} & T=127^{\circ} \mathrm{C} & T=142^{\circ} \mathrm{C} \\
t(\min ) & C_{\mathrm{A}}(\mathrm{k} / \mathrm{L}) & C_{\mathrm{A}}(\mathrm{g} / \mathrm{L}) & C_{\mathrm{A}}(\mathrm{g} / \mathrm{L}) & C_{\mathrm{A}}(\mathrm{g} / \mathrm{L}) \\
\hline ten & 8.1 & three.five & i.5 & 0.72 \\
20 & 4.3 & 1.eight & 0.76 & 0.36 \\
xxx & 3.0 & one.2 & 0.50 & 0.24 \\
twoscore & two.ii & 0.92 & 0.38 & 0.18 \\
l & 1.8 & 0.73 & 0.30 & 0.15 \\
60 & 1.5 & 0.61 & 0.25 & 0.12 \\
\hline
\terminate{array}$$

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Source: https://www.numerade.com/books/chapter/processes-and-process-variables/

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